{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MFBK4A6A76WJSZRG3OLVAJHOIO","short_pith_number":"pith:MFBK4A6A","schema_version":"1.0","canonical_sha256":"6142ae03c0ffac996626db975024ee43ad20f1d5fd49d943d1072fb46fc42a42","source":{"kind":"arxiv","id":"2607.00568","version":1},"attestation_state":"computed","paper":{"title":"FS-domains are not always RB-domains","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Hui Kou, Yuxu Chen, Zhenchao Lyu","submitted_at":"2026-07-01T07:54:13Z","abstract_excerpt":"We prove that Lawson's planar closed-disk domain is not an RB-domain. This domain is the dcpo of all closed disks in the Euclidean plane, together with the whole plane as bottom, ordered by reverse inclusion. Since this domain is an FS-domain, it gives a concrete example of an FS-domain which is not an RB-domain, answering negatively the long-standing open problem in domain theory of whether FS-domains and RB-domains are identical."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.00568","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GN","submitted_at":"2026-07-01T07:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"df191efcc7eef167f76b581b30badb3a5794db3bce0b4783810f84a8a95b11cf","abstract_canon_sha256":"ac0198441a9c5d9bb3bea1f12d621787e99e35239c9ad9ed8aa903a72e4ec67b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:47.846131Z","signature_b64":"QS9uk8Xa8nYnewtFLw+PZD2HEaUtvqOVqycB0KN8wS6rIYHd4qmibIHKEoylyooEuH7FKohnyyZNgMZlIlXhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6142ae03c0ffac996626db975024ee43ad20f1d5fd49d943d1072fb46fc42a42","last_reissued_at":"2026-07-02T01:17:47.845747Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:47.845747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"FS-domains are not always RB-domains","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Hui Kou, Yuxu Chen, Zhenchao Lyu","submitted_at":"2026-07-01T07:54:13Z","abstract_excerpt":"We prove that Lawson's planar closed-disk domain is not an RB-domain. This domain is the dcpo of all closed disks in the Euclidean plane, together with the whole plane as bottom, ordered by reverse inclusion. Since this domain is an FS-domain, it gives a concrete example of an FS-domain which is not an RB-domain, answering negatively the long-standing open problem in domain theory of whether FS-domains and RB-domains are identical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.00568","created_at":"2026-07-02T01:17:47.845814+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.00568v1","created_at":"2026-07-02T01:17:47.845814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00568","created_at":"2026-07-02T01:17:47.845814+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFBK4A6A76WJ","created_at":"2026-07-02T01:17:47.845814+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFBK4A6A76WJSZRG","created_at":"2026-07-02T01:17:47.845814+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFBK4A6A","created_at":"2026-07-02T01:17:47.845814+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO","json":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO.json","graph_json":"https://pith.science/api/pith-number/MFBK4A6A76WJSZRG3OLVAJHOIO/graph.json","events_json":"https://pith.science/api/pith-number/MFBK4A6A76WJSZRG3OLVAJHOIO/events.json","paper":"https://pith.science/paper/MFBK4A6A"},"agent_actions":{"view_html":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO","download_json":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO.json","view_paper":"https://pith.science/paper/MFBK4A6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.00568&json=true","fetch_graph":"https://pith.science/api/pith-number/MFBK4A6A76WJSZRG3OLVAJHOIO/graph.json","fetch_events":"https://pith.science/api/pith-number/MFBK4A6A76WJSZRG3OLVAJHOIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO/action/storage_attestation","attest_author":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO/action/author_attestation","sign_citation":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO/action/citation_signature","submit_replication":"https://pith.science/pith/MFBK4A6A76WJSZRG3OLVAJHOIO/action/replication_record"}},"created_at":"2026-07-02T01:17:47.845814+00:00","updated_at":"2026-07-02T01:17:47.845814+00:00"}